Step 1Roast the peppers: Place the red bell, poblano and Anaheim peppers on a rack over the flame of a stove-top burner (the restaurant chars the peppers using a blowtorch). Roast the peppers, turning to quickly char and blacken the skin on all sides (while the skin will char, the flesh should not cook); this will need to be done in batches until all of the peppers are done. When the peppers are cool enough to handle, rub the charred skin off of the peppers using kitchen or paper towels. Seed the peppers and cut each into strips. Set aside.
Step 2In a saucepot, heat one-fourth cup olive oil over medium heat. Add the shallot and cook, stirring occasionally, until translucent, 3 to 5 minutes. Add the garlic and cook until aromatic, about 1 minute. Add the chile flakes and bouquet garni, along with a pinch of salt, and stir well.
Step 3Add the red wine vinegar to the pan and increase the heat to high. Cook until the vinegar is reduced completely, 3 to 5 minutes.
Step 4Add the julienned peppers, stirring to coat them completely with oil. Season with a pinch of salt and reduce the heat. Stir in the tomatoes and season with another pinch of salt. As the tomatoes cook, they will release their juices to form a sauce.
Step 5Stir in the broth and bring the sauce to a simmer, cooking just to marry the flavors (the vegetables should keep their crunch).
Step 6Remove from heat and strain the escabeche through a colander. Spread the escabeche vegetables out onto a rimmed baking sheet to cool quickly (refrigerate if making a day in advance). Place the sauce back in the pan over medium-high heat and reduce by half. Remove from heat and, using an immersion blender, slowly emulisfy the sauce while adding the remaining one-fourth cup olive oil.
Step 7Cool the sauce completely and refrigerate until needed. The sauce is best made a day in advance to give the flavors time to marry.
Step 1Heat the oven to 300 degrees. Season the fish on both sides with a light sprinkling of salt and espellette pepper.
Step 2Over medium heat, warm a sauté pan large enough to hold the fillet of fish. Add enough oil to coat the surface of the pan and add 2 tablespoons of butter. When the butter starts to foam, carefully place the fillet in the pan. Add the garlic cloves and branch of thyme.
Step 3Cook the fish over medium heat until it is light golden in color, 3 to 4 minutes. Be very careful as the fish cooks that the pan does not get too hot and the butter does not brown too much; the fish should be tender, and heat that is too high will toughen the fillet.
Step 4Carefully flip the fillet, using 2 fish spatulas if needed. Cook an additional 3 to 4 minutes. As the fish cooks, gently baste it with the fat in the pan, spooning over the oil and butter to keep the fish moist as it cooks.
Step 5Remove the fish from the pan to a cooling rack placed on a rimmed baking sheet. Set the fish aside to rest for 3 minutes, then take the internal temperature with a thermometer. The internal temperature should read 118 degrees. If the temperature is too low, brush the fish with the softened butter and place the fish in the oven for 3 minutes. Remove the fish from the oven and rest again for 3 minutes before taking the temperature. Repeat this process until the fish reaches 118 degrees.
Step 6Strain the cooking juices from the pan, discarding the garlic and thyme and reserve for sauce.
Step 7Before serving the fish, reheat the escabeche, adding a touch more olive oil and a bit of lemon juice and/or red wine vinegar to enhance the flavors, along with the chopped parsley. Reheat the sauce, checking for seasoning and flavoring.
Step 8To serve, slice the warmed fish into 8 portions. Place the escabeche on a warmed serving platter and arrange the fish portions on top. Spoon a bit more over the fish. Serve the cooking sauce at the table.